Divide. Write the quotient in lowest terms. $\newline$ $3 \frac{3}{8} \div 9=$

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Algebra 2

Multiply and divide rational expressions

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Q. Divide. Write the quotient in lowest terms.

\newline

3 \frac{3}{8} \div 9=

Write division problem as fraction: Write the division problem as a fraction. $\newline$ We have the division problem $3\left(\frac{3}{8}\right) \div 9$ , which can be written as a fraction: $\left(3\left(\frac{3}{8}\right)\right) / 9$ .
Simplify expression inside parentheses: Simplify the expression inside the parentheses. $\newline$ The expression $3\left(\frac{3}{8}\right)$ means $3$ times $\frac{3}{8}$ , which is $\frac{9}{8}$ . $\newline$ So, the division problem now looks like this: $\left(\frac{9}{8}\right) / 9$ .
Rewrite division as multiplication by reciprocal: Rewrite the division as multiplication by the reciprocal. $\newline$ To divide by a number is the same as multiplying by its reciprocal. The reciprocal of $9$ is $\frac{1}{9}$ . $\newline$ So, the expression becomes $(\frac{9}{8}) \cdot (\frac{1}{9})$ .
Multiply numerators and denominators: Multiply the numerators and the denominators. $\newline$ When multiplying fractions, we multiply the numerators together and the denominators together. $\newline$ The numerators are $9$ and $1$ , and the denominators are $8$ and $9$ . $\newline$ So, we get $(9 \times 1) / (8 \times 9) = 9 / 72$ .
Simplify fraction to lowest terms: Simplify the fraction to its lowest terms. $\newline$ The fraction $\frac{9}{72}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is $9$ . $\newline$ $9 \div 9 = 1$ and $72 \div 9 = 8$ . $\newline$ So, the fraction simplifies to $\frac{1}{8}$ .